blackIn this paper, we extend the univariate approach of [1]} to a multivariate framework, with the objective of obtaining joint estimates of both VaR and ES for multiple financial assets simultaneously, accounting for their dependence structure. To this end, we generalize the Multivariate Asymmetric Laplace (MAL) quantile regression approach of [2]} to a time-varying setting, by allowing the parameters of the MAL to vary over time. For each asset, we model the evolution of VaR and ES as functions of the location and scale parameters of the distribution. In particular, for the VaR component, we adopt a Conditional Autoregressive Value at Risk (CAViaR) specification ([3]}).
